Testing day: The effects of processing bias induced by Navon stimuli on the strength of the Müller-Lyer illusion

Explanations for the cognitive basis of the Müller-Lyer illusion are still frustratingly mixed. To date, Day’s (1989) theory of perceptual compromise has received little empirical attention. In this study, we examine the merit of Day’s hypothesis for the Müller-Lyer illusion by biasing participants toward global or local visual processing through exposure to Navon (1977) stimuli, which are known to alter processing level preference for a short time. Participants (N = 306) were randomly allocated to global, local, or control conditions. Those in global or local conditions were exposed to Navon stimuli for 5 min and participants were required to report on the global or local stimulus features, respectively. Subsequently, participants completed a computerized Müller-Lyer experiment where they adjusted the length of a line to match an illusory-figure. The illusion was significantly stronger for participants with a global bias, and significantly weaker for those with a local bias, compared with the control condition. These findings provide empirical support for Day’s “conflicting cues” theory of perceptual compromise in the Müller-Lyer illusion.


IntroductIon
The Müller-Lyer (1889) illusion consists of two identical lines that appear different in length, due to arrowheads or arrowtails fixed at the apexes of both lines (Panel A of Figure 1). The line with the arrowheads ("fins-in") is perceived as being shorter than the line with the arrowtails ("fins-out"). Numerous theories and experimental paradigms have been explored in an attempt to explain this illusion, such as misapplied size constancy (Gregory, 1963), variations of angle degree and length of arrowheads (Dewer, 1967;Pressey & Martin, 1990;Restle & Decker, 1977), and central-tendency-effects (Pressey, 1967; see also Bertulis & Bulatov, 2001;Woloszyn, 2010).
A longstanding explanation for this illusion is that of "misapplied size constancy" (Gregory, 1963). This theory suggests that size constancy applied to objects in three-dimensional space is misapplied to two-dimensional figures due to learned depth cue confusion (see also McGraw & Stanford, 1994). The effect is typically demonstrated by comparisons between an interior room corner and an exterior building corner. Researchers have challenged this hypothesis, however, arguing that it cannot explain the illusion's persistence in dumbbell or dot presentations, where the termini of the lines cannot be conceptualised as corners or edges in three dimensions (e.g., Day, 1989;Lamy, Segal, & Ruderman, 2006;Woloszyn, 2010; see Panel A of Figure 1). Furthermore, individuals whom have little experience of linear architecture are still susceptible to the illusion; albeit to a lesser extent (Ahluwalia, 1978). Thus, there is still no consensus of explanation within the literature, particularly as many theories fail to explain various modifications of the basic illusion (see Robinson, 1998). Day (1989) proposed a theory of "perceptual compromise" to explain visual illusions like Müller-Lyer's. He suggested that the Müller-Lyer illusion arises due to conflicting cues, where a compromise exists between the true lengths of the lines and interapical distances (local features) and the lengths of the complete figures (global features). Therefore, the line with arrowtails at its apexes, or fins-out, appears longer than the line with arrowheads (or fins-in) since the fins-out figure is larger overall and the distance between the apices of the fins is greater (see Panel B of Figure 1). Although Day's mechanism is less specific regarding how the line with arrowheads at its apexes (or fins-in) might appear shorter, it would seem a natural extension of his theory to suggest that a shorter interapical distance would result in a reduction in line estimation, as the greater global feature is now concentrated in the centre of the figure (see Panel B of Figure 1). Thus, there appear to be global size differences between the two examples of the illusion, even though local features (line length) are the same. It is suggested, therefore, that a perceptual compromise is sought between this conflicting information, resulting in the illusion. Unlike some competing theories, perceptual compromise successfully accounts for illusions created by variations of the original Müller-Lyer figure. Day's theory has been proposed as an explanation for the following illusions: the Poggendorff illusion (Day & Kasperczyk, 1985), the Morinaga illusion (Day, 1989), arc and chevron illusions (Day, Jee, & Duffy, 1989), and the Bourdon illusion (Day, 1990). Other authors have described similar mechanisms which rely on mismatch, assimilation, or compromise between local features and global or gestalt figure features (e.g., Lamy et al., 2006;Morgan & Glennerster, 1991;Pressey, 1967Pressey, , 1971Woloszyn, 2010).
However, to the author's knowledge, Day's theory, or those related to it, have not seen direct empirical testing with respect to Müller-Lyer and illusion magnitude.
Interpreting Day's (1989) theory, if one were to create a bias in an observer's attention towards global processing then the magnitude of the illusion should be increased. If a participant is focusing on gestalt or global "wholes" then a compromise between the conflicting global and local cues present in the figure will be biased toward the global (overall stimulus size) cue. Conversely, if an attention bias were to exist towards local processing, thus reducing the influence of the fins, then the magnitude of the Müller-Lyer illusion should decrease, since the observer will attend more closely to the local (individual line length) cue. Navon (1977) developed a way to investigate, and bias, global and local visual processing applying a paradigm which used special stimuli, that became known as "Navon stimuli" (Figure 2). Navon used hierarchical letters, which consisted of a larger letter made up of many smaller letters. The letters could be read out in either a global form (i.e., the large letter) or in a local form (i.e., one of the small letters comprising the larger letter). Using this type of stimulus, Navon presented evidence to support the contention that global processing shows precedence over local processing; that is, global processing of a stimulus is faster and more automatic than local processing, which requires a slower and more effortful mechanism 1 . Further studies have consistently supported his results (DeLillo, Spinozzi, Palumbo, & Giustino, 2011;Fink et al., 1997;Hochstein & Ahissar, 2002;Paquet, 1992;Tanaka & Fujita, 2000;Wyer, 2010). Adding to this, Macrae and Lewis (2002) implemented Navon stimuli to modulate global and local processing before a face recognition task. Intending to prove that default face processing is generally biased toward the global level, it was found that face recognition was significantly enhanced when previously exposed to the global Navon condition, compared with the control condition. Furthermore, face recognition was significantly impaired when previously exposed to the local condition compared to the control condition. Such findings demonstrate that a processing bias can be induced by simple exposure to Navon stimuli (see also Perfect, Dennis, & Snell, 2007).
The purpose of the current study was to empirically test Day's (1989)

Materials
Participants selected into the global and local conditions were asked to view a timed presentation of Navon stimuli (created using Microsoft Visual Basic©). The stimuli appeared at a size of 500 × 500 pixels on a 21-in. widescreen LCD monitor. Three hundred Navon stimuli were made for this study (see Figure 2) and were presented individually on screen for a period of 1 s, for a total presentation time of 5 min for the whole sequence. The effects of the processing level bias modulation were then examined using a second custom-written computer program, designed to test the magnitude of the Müller-Lyer illusion. The program was written in the Microsoft Visual Basic© programming language.
The parameters for the Müller-Lyer program were as follows: For each trial, participants were asked to match the apparent length of a line between arrowheads with an adjustable comparison line (see Panel C of Figure 1). The length of the adjustable stimulus could be modified by clicking on-screen buttons marked "shorter" or "longer. " Participants were asked to click these buttons until there was a perceptual match between the adjusted line and the length of the Müller-Lyer illusion.
The adjustable comparison line was randomly set to either 100 or 200 pixels at the start of each trial to limit systematic instrumentation errors. The Müller-Lyer illusory stimulus was randomly set to between 80 and 250 pixels to prevent learning effects. The angle between the ar-rowhead lines was also varied on each trial, between 15 and 165°, in 15° increments (i.e., 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165°). Fins at angles from 15 to 75° pointed inwards (fins-in), whereas fins at angles from 105 to 165° pointed outwards (fins-out). On a given trial, a fin angle was chosen at random from the 11 possibilities, with the restriction that each angle was used eight times across the experiment, and could in this condition; whereas the gradient was shallower for the local condition, indicating a weaker illusion (see Table 1).
These observations are supported by analysis of the gradient data in SPSS. ANOVA showed a significant between-subjects main effect of condition: global, local, control; F(2, 305) = 43.97, p < .001, η 2 = .22.
Homogeneity of variance and normality were confirmed by Levene's statistic (p = .105) and the Shapiro-Wilk test (p = .845), respectively.
Post-hoc comparisons using Tukey's HSD confirmed that the global condition gradient was significantly steeper than both local and con-trol, minimum F(1, 203) = 20.89, p < .001, indicting a stronger illusion in this group. The local condition produced a gradient which was significantly shallower than global or control, minimum F(1, 203) = 23.01, p < .001, indicating a weaker illusion. Our finding appears to support the suggestion that creating a bias toward either global or local processing will influence the strength of the visual illusion, according to Day's (1989) hypothesis of perceptual compromise.

dIscussIon
The purpose of this study was to test the potential for Day's (1989) hypothesis of perceptual compromise to explain the estimation biases seen in the Müller-Lyer illusion. Day proposed that the presence of the illusion is due to a conflict between global cues and local cues.
Exposure to Navon stimuli was used to create a bias in processing level toward either global or local, before testing the illusory strength of the Müller-Lyer illusion.  Fin Angle (degrees) Mean Adjustment Error (pixels) indicates that perceptual compromise is shifted toward the overall size of the figure. Conversely, a weakening of the illusion following bias toward local processing indicates a reduction in perceptual compromise and a restored ability to accurately judge local features.
In further support of these data, studies investigating cortical activity during perception of the Müller-Lyer illusion have demonstrated that right-hemispheric visual regions, known to be global processing dominant, are more active than equivalent left-hemispheric regions, thought to be more active in local processing (e.g., Weidner, Boers, Mathiak, Dammers, & Fink, 2010;Weidner & Fink, 2007; see also Martens & Hübner, 2013). Knowing that our visual system is normally biased toward fast, global processing (Navon, 1977), it seems logical that such a pre-existing bias would influence our perception of the illusion, in terms similar to those suggested by Day (1989). Such neurallevel findings, showing that lateral occipital, interior temporal, and dorsal visual stream regions contribute to the illusion, also strengthen the contention that higher-order visual areas must be involved (thus limiting theories which rely on low-level visual properties).
It must also be noted that the "assimilation theory" of Pressey (1967,1971) bears resemblance to the ideas put forward by Day (1989).
Pressey's assimilation theory argues that the length of the central line is misperceived, since the visual system cannot successfully isolate local feature parts from global wholes (but see also Howe & Purves, 2005).
Technically therefore, the end point of this theory is the same as Day predicts: A line with fins-out is seen as longer because the stimulus is, effectively, longer. Our Navon manipulation, when participants focus on the local letter features, may thus allow more effective featural isolation in the illusion, which would have the same outcome as reduced global compromise.
Furthermore, from these data it is not impossible to discount Gregory's (1963) misapplied size constancy theory. For example, when a bias is formed toward the local features of the stimulus, this situation may reduce the likelihood that the figure would produce the threedimensional global gestalt that -as Gregory suggests -is responsible for the impression of depth (and thus the application of size constancy) in the illusion. In effect, the manipulation of global and local bias may be modifying the extent to which the features of the figure are seen as distinct from one another, or as a whole.
It is clear from the plethora of theory and empirical data on the Müller-Lyer illusion and related visual phenomena that simple mechanistic explanations are unlikely to capture the full scope of their neural or cognitive basis. Further investigation is of course required to examine the effect described here in more detail. For example, eye tracking information would be very useful in determining any change in fixation or scan-pattern of the illusion following a Navon-like processing level manipulation.

Footnotes
1 One can see, therefore, how such an arrangement may bring about Day's perceptual compromise with regard to visual illusion: A pre-disposition to process global information before local detail will precipitate into the "conflicting cues" scenario.